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Risk measures and their applications in portfolio optimization

Birbil, Ş. İlker and Frenk, J.B.G. and Kaynar, Bahar and Noyan, Nilay (2008) Risk measures and their applications in portfolio optimization. In: Gregoriou, Greg N., (ed.) Measuring Financial Risk: A VaR Approach. The McGraw-Hill Publishers, New York. (Accepted/In Press)

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Abstract

Several approaches exist to model decision making under risk, where risk can be broadly defined as the effect of variability of random outcomes. One of the main approaches in the practice of decision making under risk uses mean-risk models; one such well-known is the classical Markowitz model, where variance is used as risk measure. Along this line, we consider a portfolio selection problem, where the asset returns have an elliptical distribution. We mainly focus on portfolio optimization models constructing portfolios with minimal risk, provided that a prescribed expected return level is attained. In particular, we model the risk by using Value-at- Risk (VaR) and Conditional Value-at-Risk (CVaR). After reviewing the main properties of VaR and CVaR, we present short proofs to some of the well-known results. Finally, we describe a computationally efficient solution algorithm and present numerical results. Keywords: Elliptical distributions; mean-risk; value-at-risk; conditional value-at-risk; portfolio optimization

Item Type:Book Section / Chapter
Uncontrolled Keywords:Elliptical distributions; mean-risk; value-at-risk; conditional value-at-risk; portfolio optimization.
Subjects:Q Science > Q Science (General)
ID Code:9657
Deposited By:Nilay Noyan
Deposited On:07 Nov 2008 16:50
Last Modified:20 Nov 2009 10:14

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